Parallelization of Hierarchical Matrix Algorithms for Electromagnetic Scattering Problems

Elisabeth Larsson (1, 2) , Afshin Zafari (2, 1) , Marco Righero (3) , M. Alessandro Francavilla (4) , Giorgio Giordanengo (3) , Francesca Vipiana (5) , Giuseppe Vecchi (5) , Christoph Kessler (6) , Corinne Ancourt (7, 8) , Clemens Grelck (9)

1 Uppsala University
2 DIT-UPPSALA - Department of Information Technology
3 LACE - Antenna and Electromagnetic Compatibility Laboratory (Politecnico di Torino)
4 ASML Netherlands BV, De Run 6501, NL-5504 DR Veldhoven, Netherlands
5 DET - Department of Electronics and Telecommunications [Torino]
6 Department of Computer and Information Science - Linköping University
7 CRI - Centre de Recherche en Informatique
8 Mines Paris - PSL (École nationale supérieure des mines de Paris)
9 UNIVERSITY OF AMSTERDAM - ISLA - Informatics Institute

Numerical solution methods for electromagnetic scattering problems lead to large systems of equations with millions or even billions of unknown variables. The coefficient matrices are dense, leading to large computational costs and storage requirements if direct methods are used. A commonly used technique is to instead form a hierarchical representation for the parts of the matrix that corresponds to far-field interactions. The overall computational cost and storage requirements can then be reduced to O(N log N). This still corresponds to a large-scale simulation that requires parallel implementation. The hierarchical algorithms are rather complex, both regarding data dependencies and communication patterns, making parallelization non-trivial. In this chapter, we describe two classes of algorithms in some detail, we provide a survey of existing solutions, we show results for a proof-of-concept implementation, and we provide various perspectives on different aspects of the problem. The list of authors is organized into three subgroups, Larsson and Zafari (coordination and proof-of-concept implementation), Righero, Francavilla, Giordanengo, Vipiana, and Vecchi (definition of and expertise relating to the application), Kessler, Ancourt, and Grelck (perspectives and parallel expertise).

Domaines: Electromagnétisme; Parallélisation; Calcul parallèle, distribué et partagé [cs.DC]; Informatique et société

Elisabeth Larsson, Afshin Zafari, Marco Righero, M. Alessandro Francavilla, Giorgio Giordanengo, et al.. Parallelization of Hierarchical Matrix Algorithms for Electromagnetic Scattering Problems. High-Performance Modelling and Simulation for Big Data Applications, pp.36-68, 2019, 978-3-030-16272-6. ⟨10.1007/978-3-030-16272-6_2⟩. ⟨hal-02135894⟩